FUNDAMENTALS OF ROCK MECHANICS
CONTENTS 1 ROCK AS A MATERIAL INTRODUCTION JOINTS AND FAULTS ROCK-FORMING MINERALS THE FABRIC OF ROCKS THE MECHANICAL NATURE OF ROCK 2 ANALYSIS OF STRESS AND STRAIN DE?NITION OF TRACTION AND STRESS ANALYSIS OF STRESS IN TWO DIMENSIONS GRAPHICAL REPRESENTATIONS OF STRESS IN TWO DIMENSIONS STRESSES IN THREE DIMENSIONS STRESS TRANSFORMATIONS IN THREE DIMENSIONS MOHR’S REPRESENTATION OF STRESS IN THREE DIMENSIONS STRESS INVARIANTS AND STRESS DEVIATION DISPLACEMENT AND STRAIN 2 10 IN?NITESIMAL STRAIN IN TWO DIMENSIONS 2 11 IN?NITESIMAL STRAIN IN THREE DIMENSIONS 2 12 DETERMINATION OF PRINCIPAL STRESSES OR STRAINS FROM MEASUREMENTS 2 13 COMPATIBILITY EQUATIONS 2 14 STRESS AND STRAIN IN POLAR AND CYLINDRICAL COORDINATES 2 15 FINITE STRAIN 3 FRICTION ON ROCK SURFACES AMONTON’S LAW FRICTION ON ROCK SURFACES STICK–SLIP OSCILLATIONS SLIDING ON A PLANE OF WEAKNESS EFFECTS OF TIME AND VELOCITY 4 DEFORMATION AND FAILURE OF ROCK THE STRESS–STRAIN CURVE EFFECTS OF CON?NING STRESS AND TEMPERATURE TYPES OF FRACTURE COULOMB FAILURE CRITERION MOHR’S HYPOTHESIS EFFECTS OF PORE ?UIDS FAILURE UNDER TRUE-TRIAXIAL CONDITIONS THE EFFECT OF ANISOTROPY ON STRENGTH 5 LINEAR ELASTICITY STRESS–STRAIN RELATIONS FOR AN ISOTROPIC LINEAR ELASTIC SOLID SPECIAL CASES HOOKE’S LAW IN TERMS OF DEVIATORIC STRESSES AND STRAINS EQUATIONS OF STRESS EQUILIBRIUM EQUATIONS OF STRESS EQUILIBRIUM IN CYLINDRICAL AND SPHERICAL COORDINATES AIRY STRESS FUNCTIONS ELASTIC STRAIN ENERGY AND RELATED PRINCIPLES UNIQUENESS THEOREM FOR ELASTICITY PROBLEMS 5 10 STRESS–STRAIN RELATIONS FOR ANISOTROPIC MATERIALS 6 LABORATORY TESTING OF ROCKS HYDROSTATIC TESTS UNIAXIAL COMPRESSION TRIAXIAL TESTS STABILITY AND STIFF TESTING MACHINES TRUE-TRIAXIAL TESTS DIAMETRAL COMPRESSION OF CYLINDERS TORSION OF CIRCULAR CYLINDERS BENDING TESTS 6 10 HOLLOW CYLINDERS 7 POROELASTICITY AND THERMOELASTICITY HYDROSTATIC POROELASTICITY UNDRAINED COMPRESSION CONSTITUTIVE EQUATIONS OF POROELASTICITY EQUATIONS OF STRESS EQUILIBRIUM AND ?UID ?OW ONE-DIMENSIONAL CONSOLIDATION APPLICATIONS OF POROELASTICITY THERMOELASTICITY 8 STRESSES AROUND CAVITIES AND EXCAVATIONS COMPLEX VARIABLE METHOD FOR TWO-DIMENSIONAL ELASTICITY PROBLEMS HOMOGENEOUS STATE OF STRESS PRESSURIZED HOLLOW CYLINDER CIRCULAR HOLE IN A ROCK MASS WITH GIVEN FAR-?ELD PRINCIPAL STRESSES STRESSES APPLIED TO A CIRCULAR HOLE IN AN IN?NITE ROCK MASS STRESSES APPLIED TO THE SURFACE OF A SOLID CYLINDER INCLUSIONS IN AN IN?NITE REGION ELLIPTICAL HOLE IN AN IN?NITE ROCK MASS 8 10 STRESSES NEAR A CRACK TIP 8 11 NEARLY RECTANGULAR HOLE 8 12 SPHERICAL CAVITIES 8 13 PENNY-SHAPED CRACKS 8 14 INTERACTIONS BETWEEN NEARBY CAVITIES 9 INELASTIC BEHAVIOR PLASTICITY AND YIELD ELASTIC–PLASTIC HOLLOW CYLINDER CIRCULAR HOLE IN AN ELASTIC–BRITTLE–PLASTIC ROCK MASS PERFECTLY PLASTIC BEHAVIOR FLOW BETWEEN ?AT SURFACES FLOW RULES AND HARDENING CREEP SIMPLE RHEOLOGICAL MODELS 9 10 THEORY OF VISCOELASTICITY 9 11 SOME SIMPLE VISCOELASTIC PROBLEMS 10 MICROMECHANICAL MODELS 10 1 INTRODUCTION 10 2 EFFECTIVE MODULI OF HETEROGENEOUS ROCKS 10 3 EFFECT OF PORES ON COMPRESSIBILITY 10 4 CRACK CLOSURE AND ELASTIC NONLINEARITY 10 5 EFFECTIVE MEDIUM THEORIES 10 6 SLIDING CRACK FRICTION AND HYSTERESIS 10 7 GRIF?TH CRACKS AND THE GRIF?TH LOCUS 10 8 LINEAR ELASTIC FRACTURE MECHANICS 10 9 GRIF?TH THEORY OF FAILURE 11 WAVE PROPAGATION IN ROCKS 11 1 INTRODUCTION 11 2 ONE-DIMENSIONAL ELASTIC WAVE PROPAGATION 11 3 HARMONIC WAVES AND GROUP VELOCITY 11 4 ELASTIC WAVES IN UNBOUNDED MEDIA 11 5 RE?ECTION AND REFRACTION OF WAVES AT AN INTERFACE 11 6 SURFACE AND INTERFACE WAVES 11 7 TRANSIENT WAVES 11 8 EFFECTS OF ?UID SATURATION ATTENUATION 11 10 INELASTIC WAVES 12 HYDROMECHANICAL BEHAVIOR OF FRACTURES GEOMETRY OF ROCK FRACTURES NORMAL STIFFNESS OF ROCK FRACTURES BEHAVIOR OF ROCK FRACTURES UNDER SHEAR HYDRAULIC TRANSMISSIVITY OF ROCK FRACTURES COUPLED HYDROMECHANICAL BEHAVIOR SEISMIC RESPONSE OF ROCK FRACTURES FRACTURED ROCK MASSES 13 STATE OF STRESS UNDERGROUND SIMPLE MODELS FOR THE STATE OF STRESS IN THE SUBSURFACE MEASURED VALUES OF SUBSURFACE STRESSES SURFACE LOADS ON A HALF-SPACE: TWO-DIMENSIONAL THEORY SURFACE LOADS ON A HALF-SPACE: THREE-DIMENSIONAL THEORY HYDRAULIC FRACTURING OTHER STRESS-MEASUREMENT METHODS 14 GEOLOGICAL APPLICATIONS STRESSES AND FAULTING OVERTHRUST FAULTING AND SLIDING UNDER GRAVITY STRESSES AROUND FAULTS MECHANICS OF INTRUSION BEAM MODELS FOR CRUSTAL FOLDING EARTHQUAKE MECHANICS REFERENCES